Variable is normally distributed
by Kolmogorov-Smirnoff goodness-of fit test.
To demonstrate that the data are approximately normally distributed
, Figs, 1a and lb display the skew and kurtosis (shown as differences from 3, the kurtosis of a normal distribution) of 36 daily values along the tracks of each polar party.
The experimental errors are assumed to be independently and normally distributed
. Estimation of parameters and statistical inferences can be possible if and only if this assumption is valid.
If we assume our process is normally distributed
, and measure Pp = 2.0 (Six-Sigma process), this means we are predicting extremely low ppm levels of defects: less than 0.002 ppm (3.4 ppm with the irritating 1.5 shift).
Shapiro-Wilk univariate normality tests indicated that total hours of sleep were not normally distributed
at the time of the pretests (Table 1).
Thus, we present the calculation process of paired t-test and independent t-test in the data analysis, respectively, under the assumption that both samples come from normally distributed
populations with unknown but equal variances.
Comparisons between normally distributed
data were done using Student's t-test; for data not normally distributed
we used the Wilcoxon Mann-Whitney U-test.
At 0.01 significance level of alpha, the critical values of chi square distribution with 2 degrees of freedom must be less than 9.21 under Jarque-Bera test for a normally distributed
One of them, which have different time-sequence phases and multiple attribute indexes of normally distributed
stochastic variables, like street traffic flow, shopping centre popularity at different times, or the customer waiting times, is referred to as dynamic stochastic multiattribute decisionmaking problems.
An unpaired two-tailed i-test based on ranks (Mann-Whitney) was used to compare differences between two groups for data that were not normally distributed
and a two-tailed unpaired Student's i-test was used for normally distributed
The simple assumption that the measurement errors are normally distributed
does not lead to a statistically normal distribution, but to a "Cauchy," "ratio," or "Lorentzian" distribution, which cannot be parameterized like a normal distribution since it contains infinite values when the denominator goes to zero .
The latitude variations in the zero meridian are simulated by the same time series of polar motion plus a model of normally distributed
random errors N(0, 0.1 as), based on Forsythe, Malcolm and Moler algorithm (Forsythe et al., 1977).